RETURN TIME AND VULNERABILITY FOR A FOOD-CHAIN MODEL

Simulation studies have shown that the time it takes for a system of interacting species in a food chain to return to equilibrium after a disturbance increases as the number of trophic levels increase. It has been argued that this effect is important in limiting the length of food chains subject to perturbations of the real world. We show that for an asymptotically stable system a lower bound on the return time is directly proportional to the number of trophic levels in agreement with simulation studies. In addition, the lower bound on the return time is shown to be inversely proportional to the sum of products of the intraspecific competition coefficient and equilibrium population of the species. A new method for directly computing the vulnerability of a system to external perturbations is presented. Using this method we demonstrate that for a food chain where the number of species is equal to the number of trophic levels, the return time alone is not a proper measure of system vulnerability. Indeed, adding an additional trophic level may make the system less vulnerable to disturbances. Interspecific coupling between the trophic levels is shown to be an important factor in determining system vulnerability. © 1979.